Graphs whose maximum clique size exceeds half of the total number of vertices satisfy a classical property: the family of their maximum sized cliques can be pierced by a single vertex. This result dates back to a 1965 theorem by Hajnal. Motivated by this theorem, Jung, Keszegh, Pálvölgyi, and Yuditsky recently conjectured that an analogous result should hold for hypergraphs of larger uniformity, with an appropriate constant replacing the threshold $1/2$. In this paper we refute this conjecture in a strong form. We show that for any constant $c<1$ and integers $k\ge 3$ and $t\ge 1$, there exist $k$-uniform hypergraphs $G$ whose maximum clique size exceeds $c|V(G)|$, yet the family of maximum size cliques of $G$ cannot be pierced by $t$ vertices. This demonstrates that no universal constant threshold guarantees bounded piercing number for maximum cliques in uniform hypergraphs. We discuss further questions concerning the relationship between clique size and piercing maximum cliques in hypergraphs, and introduce a geometric variant of the problem using Helly's Theorem.

Cell-free multiple-input multiple-output (CF-MIMO) architecture significantly enhances wireless network performance, offering a promising solution for delay-sensitive applications. This paper investigates the resource allocation problem in CF-MIMO systems, aiming to maximize energy efficiency (EE) while satisfying delay violation rate constraint. We design a Proximal Policy Optimization (PPO) with a primal-dual method to solve it. To address the low sample efficiency and safety risks caused by cold-start of the designed safe deep reinforcement learning (DRL) method, we propose a novel offline pretraining framework based on virtual constrained Markov decision process (CMDP) modeling. The virtual CMDP consists of reward and cost prediction module, initial-state distribution module and state transition module. Notably, we propose an evidence-aware conditional Gaussian Mixture Model (EA-CGMM) inference approach to mitigate data sparsity and distribution drift issues in state transition modeling. Simulation results demonstrate the effectiveness of CMDP modeling and validate the safety and efficiency of the proposed pretraining framework. Specifically, compared with non-pretrained baseline, the agent pretrained through our proposed framework achieves twice the initial EE and maintains a low delay constraint violation rate of $1\%$, while ultimately converging to an EE that is $4.7\%$ higher with a $50\%$ reduction in exploration steps. Additionally, our proposed pretraining framework implementation exhibits comparable performance to the SOTA diffusion model-based implementation, while achieving a $14$-fold reduction in computational complexity.

Efficient beam alignment is fundamental to high-throughput and reliable connectivity in Vehicle-to-Everything (V2X) systems. However, conventional beam management in dynamic vehicular topologies incurs prohibitive alignment overhead and struggles to maintain robust links under rapid mobility. To overcome these challenges, this paper proposes a distributed multimodal graph beam alignment (GBA) framework. The core innovation lies in leveraging onboard multimodal sensing data to predict implicit feedback while employing graph neural networks to coordinate multi-user alignment, thereby jointly enhancing scalability and drastically reducing overhead. The architecture adopts a dual-network design with GBA-RSU and GBA-Vehicle units, optimized through a hybrid strategy of centralized learning and federated learning (FL) to balance global performance with local privacy. Furthermore, a dedicated data augmentation (DA) scheme is introduced to address multimodal data imbalance issues in vehicular networks. Negative augmentation applies dominant modality dropout to bolster robustness, while positive augmentation generates underrepresented samples to mitigate label imbalance. Numerical results demonstrate that GBA maintains a competitive sum rate on par with high-resolution codebook-based feedback yet reduces beam alignment overhead by over 90\% and scales efficiently in mobile scenarios. Notably, integrating DA enables GBA to consistently outperform state-of-the-art FL-based alignment benchmarks, with particularly pronounced gains under severe label and modality imbalance, establishing a practical solution for V2X beam management.

We derive the classical Gibbs measure on $\mathbb{T}^2$ associated with the fractional Bessel interaction potential $\widehat{v}_β(k)=\langle k\rangle^{-β}$ from a renormalized grand-canonical quantum Bose gas with the same interaction. Our result covers the whole range $\frac32<β\leq2$, where $\widehat{v}_β(k)$ is not summable and the quantum model cannot be written in the usual density-square form, as the associated self-energy diverges. We therefore need to renormalize the zero mode by a centered number-fluctuation term and then develop a detailed analysis for the high-frequency remainders. All this allows us to implement a low-frequency localization and obtain the convergence of the quantum relative free energy to the classical fractional-Bessel free energy, as well as the convergence of the reduced density matrices to the limiting Gibbs measure.

Let $-Δ_{\mathbb{H}}+V$ be the Schrödinger operator on $\mathbb{H}$ where $V \in L^p(\mathbb{H}) \cap L^\infty(\mathbb{H})$ for some $p > 0$. If $(X_n)$ is a uniformly discrete sequence of compact hyperbolic surfaces with a uniform spectral gap that Benjamini-Schramm converges to $\mathbb{H}$, we prove quantum mixing for the eigenfunctions of $-Δ_{X_n}+V_n$ in any sufficiently large spectral window $I$, where $V_n$ is the potential on $X_n$ induced by $V$. These apply to large degree lifts of a potential on a base surface such as congruence covers of arithmetic surfaces, with high probability to random hyperbolic surfaces in the Weil-Petersson model of large genus, and to Hartree one-particle operators arising in thermodynamic limit of many-body Bose gas on hyperbolic surfaces. The proof uses the Duhamel formula for the hyperbolic wave equation together with exponential mixing of the geodesic flow on $T^1 X_n$.

We investigate the optimal execution of contracts that are used in merger\&acquisition deals. We consider cash-settled and physically delivered contracts between a broker and a counterpart. Contracts are linear (total returns swaps), nonlinear (collar contracts) or Asian type (TWAP based contracts). We derive the optimal execution strategy and the optimal fee through indifference utility arguments allowing for linear market effects of trades. We show that linear cash-settled contracts are more expensive and more exposed to manipulation/statistical arbitrages by the broker. Also nonlinear and Asian type contracts are exposed to these phenomena.

This paper studies a multiple-input multiple-output (MIMO) radar system for sensing the unknown and random angular location (angle) of a point target, based on the target-reflected echo signals and known prior distribution information about the target's angle specified by a probability density function (PDF). We consider a challenging yet practical scenario where the knowledge of such PDF is imperfect, due to the inaccuracy in PDF acquisition or unpredicted change of target appearance pattern; while the real (actual) PDF is modeled as an unknown perturbed version of the imperfect known PDF bounded by a given uncertainty radius. Such PDF imperfection motivates us to study the robust transmit beamforming design to optimize the worst-case sensing performance among all possible real PDFs. Since the sensing mean-squared error (MSE) is difficult to be characterized explicitly, we adopt the worst-case posterior Cramér-Rao bound (PCRB) as the performance metric. We formulate the beamforming optimization problem to minimize the maximum PCRB among all possible real PDFs, which is highly non-trivial since the PCRB has a complex intractable expression over the real PDF, and there are infinite constraints corresponding to the continuous set of real PDFs bounded by the uncertainty radius. To address these challenges, we derive a tractable quadratic approximation of the PCRB via second-order Taylor expansion, and leverage the S-procedure to equivalently transform the infinite constraints into a linear matrix inequality, based on which the problem is reformulated into a convex optimization problem solvable with polynomial time complexity. The obtained solution approaches the globally optimal robust beamforming solution as the uncertainty radius decreases. Numerical results validate the effectiveness of our proposed robust beamforming design.

This paper is dedicated to the analysis of infinite horizon optimal control problems subject to semilinear parabolic equations with constraints on the controls and discounted cost functionals. The discount factors on the cost and the state components are allowed to differ from each other. First-order as well as second-order optimality conditions are derived and the importance of allowing different discount factors for the second-order analysis for the class of nonlinearities under consideration is demonstrated. Finally convergence and rate of convergence for the approximation of the infinite horizon problem by a family of finite horizon problems is proven.

For a graph $G$ and partition $\mathcal{U}$ of its vertex set, an independent transversal of $(G, \mathcal{U})$ is an independent set of $G$ that contains one vertex from each block of $\mathcal{U}$. Buys, Kang, and Ozeki studied when a reconfiguration graph on independent transversals of $(G,\mathcal{U})$ is connected, meaning any independent transversal can be transformed into any other one through a sequence of one-vertex modifications while always maintaining an independent transversal. Analogous to a theorem of Haxell, they proved that this is the case if $G$ has maximum degree $Δ$ and each block of $\mathcal{U}$ has size at least $2Δ$, except if the union of some $k \ge 1$ blocks of $\mathcal{U}$ induces $k$ disjoint copies of the complete bipartite graph $K_{Δ, Δ}$ in $G$. Solving one of their problems, we exactly characterize the partition structure in the latter exceptional instances of their theorem, showing that there is a rich variety of them but they are generated by a simple constructive procedure.

We propose a semiclassical framework for solving open quantum dynamics in driven-dissipative spin systems. Our method consists of generalized spin-wave approximations tailored to describing quantum trajectories unravelled from the master equation, and generically applies to regimes beyond the reach of conventional spin-wave theories, including short-range interactions and local quantum jumps, enabling the efficient simulation of large-scale interacting spins. We illustrate the versatility of our framework by studying a variable-range driven-dissipative Ising model on a 2D lattice. When the dissipation acts along the drive axis, we find a continuous phase transition breaking the $\mathbb{Z}_2$ symmetry, and demonstrate that the interaction range, when tuned from fully-connected to nearest-neighbour, profoundly alters the universality class of the criticality. With the dissipation along the interaction axis, we show the emergence of a first-order transition. Demonstrated with both state-diffusion and quantum-jump types of trajectory dynamics, our framework provides a powerful toolbox for the efficient semiclassical description of non-equilibrium dynamics and many-body phases in spin systems.

Program verification is a formal technique to rigorously ensure the correctness and fault-freeness of software systems. However, constructing comprehensive interprocedural specifications for full verification obligations is time-consuming and labor-intensive, giving rise to automated specification generation approaches. Despite the significant advancements in these approaches brought by Large Language Models (LLMs), existing LLM-empowered approaches still suffer from significant limitations: they lack effective strategies for handling sizable input programs, and are typically equipped with no mechanisms to evaluate and guarantee the strength of the generated specifications. The limitations impair their ability to extract precise specifications from real-world complicated programs to support the verification of target properties, thereby hindering the applicability of existing approaches in verification tasks on real-world programs. To remedy this gap, we propose SpecSyn, a novel LLM-based specification generation method. SpecSyn first decomposes the input program into individual segments, which are handled respectively by the subsequent iterative specification generation process. Innovatively, we incorporate into the process a specification refinement mechanism based on semantic-non-equivalent program mutations and variant discrimination, assessing and enhancing the semantic strength of the generated specifications. Extensive experiments show that SpecSyn maintains high precision over 90% and outstanding recall over 75%, significantly outperforming existing LLM-based approaches. In further evaluations, SpecSyn successfully handles 1071 out of 1365 target properties for open-source programs, proving its applicability on real-world program verification tasks.

Biodiversity loss is accelerating at an unprecedented pace, threatening ecosystem stability, economic resilience, and human well-being, with billions required to reverse current trends. Against this backdrop, biodiversity finance has emerged as a rapidly expanding but highly fragmented field spanning ecology, economics, finance, accounting, and policy. However, it remains emerging and complex, with the majority of relevant knowledge being produced in non-finance journals. This study employs quantitative bibliometric analysis to examine a corpus of 189,456 references underlying 3,998 articles related to biodiversity and finance. The analysis identifies eight primary research streams within the field that concern (1) strategic and financial approaches in global biodiversity conservation, (2) the impact and implementation of payments for environmental services (PES) in developing countries, (3) neoliberal influences and implications in environmental conservation, (4) biodiversity offsets and conservation, (5) ecosystem services and biodiversity, (6) integrating conservation and community interests in biodiversity management, (7) balancing agricultural intensification with biodiversity conservation, and (8) global and corporate biodiversity reporting. The characteristics of each research stream and its prevalent publications are outlined, alongside an analysis of their temporal evolution and the degree of information exchange among the research streams. The findings provide a structured map of the intellectual architecture of biodiversity finance, document pronounced silos between economically-oriented and critical/political-economy research streams, and translate these patterns into a focused research agenda and implications for policymakers, financial institutions, and corporate actors.

High-fidelity control of superconducting qubits requires carefully shaped microwave pulses that account for multiple error channels. In this work, we present a pedagogical introduction to pulse-shaping techniques for transmon qubits, aiming to provide a unified, accessible framework that integrates physical intuition for pulse design, analytical understanding of gate-level descriptions, and practical considerations of hardware. This article further aims to serve as a guide for students and early researchers entering superconducting quantum computing. We begin by examining simple pulse envelopes and their spectral properties, highlighting how finite bandwidth leads to leakage outside the computational subspace. These observations motivate the introduction of the derivative removal by adiabatic gate (DRAG) technique, which uses a quadrature component proportional to the pulse's time derivative to suppress off-resonant excitations. We analyze the single-qubit case using the Magnus expansion, which provides a clear understanding of the order-by-order introduction of error channels. We discuss the practical hardware realities of control pulse generation, focusing on arbitrary waveform generators (AWG), local oscillators (LO), and IQ mixing. Common imperfections are discussed in terms of their impact on the effective pulse shape and qubit Hamiltonian. Finally, we extend the discussion to two-qubit operations, focusing on the cross-resonance gate and the emergence of effective interactions.

In recent years, a method for computing spin dynamics at infinite temperature (spinDMFT) was developed. It utilizes the ideas of dynamical mean-field theory for fermions: single-site approximation and a self-consistency condition to approximate time-dependent spin correlations. In this work, we develop a crucial extension of the method to systems at finite temperature, able to compute imaginary-time correlations and thermodynamical quantities. We benchmark the method by comparison to results in finite-size systems, obtaining very good agreement with correlations in a random-coupling system, good agreement for a ferromagnetic system and large discrepancies in the case of an antiferromagnet. We note the appearance of ferromagnetic order in the method. We discuss possible extensions and potential applications of the approach.

The three-dimensional (3D) topological insulators (TIs), hosting topologically protected helical surface states, can be promoted into second-order TIs when a diagonal Zeeman term, typical of magnetic doping, is introduced. The latter hosts exotic chiral one-dimensional (1D) topological hinge states (THSs). In this paper, we investigate the electronic transport of THSs through a magnetic domain wall (DW) in a 3D TI nanowire. Due to the sign reversal of the out-of-plane magnetization across the DW, four 1D topological boundary states, residing on the edge of the DW, arise and form an enclosed loop mediating the counterpropagating THSs. By applying a uniform magnetic field parallel to the nanowire, we obtain a perfect sinusoidal Aharonov-Bohm oscillation in the two-terminal conductance $G$, formulated by $G=\frac{e^2}{2h} \left[ 1- \cos(πΦ/Φ_0) \right]$, with $Φ$ the magnetic flux through the DW and $Φ_0 = h/2e$ the flux quantum. Applying a phenomenological scattering matrix approach, we explain this novel Aharonov-Bohm oscillation perfectly, and attribute the constructive (destructive) interference of transmission at $Φ= Φ_0$ (0) to the $π$-spin rotation of the THSs traveling through the DW. Extending our study to a double-DW junction, where the central region has antiparallel magnetization to the leads, we observe Fabry-P{é}rot oscillations, in which the conductance minima are tuned by the magnetic flux. Our findings open a new avenue for finely controlling the quantum transport of THSs in magnetic systems using magnetic flux, and provide a faithful way for detecting THSs in experiments.

Recent experiments found superconductivity in nonmagnetic MnB$_4$ with a high critical temperature ($T_{c}$) reaching 14 K at 158 GPa. However, ab initio calculations of the electron-phonon coupling predict a $T_{c}$ below 1 K, suggesting that a conventional mechanism cannot explain this phenomenon. In this Letter, we find that MnB$_4$ is close to an altermagnetic instability in density-functional theory calculations. We propose that the superconductivity is driven by altermagnetic spin fluctuations. To verify the pairing symmetry, we have constructed a two-orbital tight-binding model, where boron states at the Fermi level are integrated out. Using this model, we identify an extended-$s$ symmetry as the leading pairing instability. If confirmed, this will be the first reported case of superconductivity driven by altermagnetic spin fluctuations.

We construct mode-selective effective models describing the interaction of the quantum plasmon-polariton field supported by a finite dielectric medium and one or several quantum emitters. The construction of the effective model is based on the decomposition of the field into bright modes relevant to the interaction with the emitters and dark modes, which do not interact with the emitters. We show that the quantum plasmon-polariton field can be represented equivalently by a double-continuum spectrum or by a single hybrid continuum spectrum for each emitter. The system of the electromagnetic field coupled to a finite medium is composed of two families of continuum modes, each of them with an infinite degeneracy. The two families are deformations of the free electromagnetic field and the free medium, induced by the interaction between them, as described by the Lippmann-Schwinger equations. We show that if there are $N$ emitters interacting with this plasmon-polariton field, the effective interaction involves a much smaller set of bosonic continuum modes: the interacting part of the continuum can be described by $N$ non-degenerate one-dimensional continua, one for each emitter. The representation of the interaction in terms of a single hybrid continuum spectrum coincides with the one within the macroscopic Langevin model with bulk medium. This coincidence is explained by an exact compensation of two terms, one in the coupling term of the Hamiltonian and the other one in a Green tensor identity.

Context: ASPIICS is a giant-baseline visible light solar coronagraph, which relies on the millimetric positioning performance of the precision formation flying Proba-3 mission of the European Space Agency. Proba-3 was launched on 5 Dec 2024, and since then ASPIICS observes the solar corona with the field of view (1.1-3) R_sun. Aims: Diffraction, in particular diffraction of solar disk light on the external occulter, is known to provide a major source of straylight in coronagraphs. We aim to analyze diffracted light visible in ASPIICS images, compare it with the analytical-numerical diffraction model reported earlier, and fine-tune the model. Methods: We compare diffraction effects visible in ASPIICS data with simulated diffraction images; in particular, we compare the geometrical properties and the radiometric signal. The properties of the diffraction described in previous works suggest how to fine-tune the model in order to achieve a better correspondence with the observations. Results: Early ASPIICS observations, where diffraction is pronounced, fully confirm all the qualitative properties of diffracted light suggested by the model. After fine-tuning of the model we see quantitative correspondence of the level of 30\% -- 50\%, depending on the configuration. Conclusions: The performed analysis allows (a) to validate our analytical-numerical model and justify the assumptions, and (b) to estimate the contribution of the diffracted light in the ASPIICS images. In the majority of the field of view the diffracted light is two orders of magnitude below the coronal signal.

We analyze a dual mixed nonconforming discretization of a generalized Darcy-Forchheimer model. Compared to the analogous scheme proposed by Girault and Wheeler, we consider general, i.e., nonquadratic, Forchheimer nonlinearities; we admit mixed, inhomogeneous boundary conditions; we allow for more general, i.e., with lower Lebesgue regularity, permeability tensors; we construct general-order schemes; we prove convergence to the exact solution under low regularity assumptions, based on novel Sobolev-trace inequalities for broken spaces; we derive error estimates of general-order assuming extra regularity of the exact solution and data; we present numerical results assessing the performance of the proposed schemes for different types of nonlinearity and nonlinear solvers.

We present the first high-resolution spectroscopy of the black hole high-mass X-ray binary Cygnus X-1 with XRISM, including orbital-phase-resolved analyses and tentative evidence of short-term variability in the Fe-K band on second timescales. Using data from the Performance Verification phase in April 2024, we analyzed spectral variability across orbital phases with the Resolve microcalorimeter and the Xtend CCD imager. The unprecedented resolution of Resolve reveals variability in highly ionized Fe absorption lines. The absorption features show orbital-phase-dependent variability in column density, ionization state, and blueshifted velocity, suggesting structural variations in the focused stellar wind along the line of sight. We also find indications of subtle broadening of the neutral Fe emission profile. In addition, intensity-sorted spectroscopy during dip phases suggests possible variability on timescales of a few seconds in the absorption features, consistent with cooler, denser and lower-ionized gas clumps. Although the statistical significance is limited, these results hint that the stellar wind and the X-rays from the accretion disk around the black hole may interact on timescales as short as a few seconds. These XRISM results constrain wind-fed accretion in Cyg X-1 and highlight Resolve's capability to probe plasma environments in high-mass X-ray binaries.

In this paper, we investigate the non-symmetric Strong Spectral Property (nSSP) from a combinatorial perspective. To zero-nonzero patterns of matrices we associate directed graphs and study when they require or allow the nSSP, providing a framework that avoids verifying the nSSP for individual matrices. A new combinatorial method is introduced and used to recognise several patterns that require the nSSP. It is shown that loop assignments in double paths play a critical role in establishing this property, and we show that an open question regarding irreducible tridiagonal patterns has a negative answer. We also investigate whether the minimum number of arcs in a directed graph on $n$ vertices that requires the nSSP, is equal to $2n-1$, and confirm this minimum for several specific digraph families.

Given a hypergraph $F$, what is the largest chromatic number that an $F$-free hypergraph can have? In the case of graphs, this question is easy to answer: the chromatic number is unbounded if $F$ contains a cycle, and the largest chromatic number of $F$-free graphs is $k-1$ if $F$ is a forest on $k$ vertices. The situation is more complicated for hypergraphs. The strong coloring of a hypergraph is a coloring of the vertices such that every hyperedge is rainbow. The weak coloring of a hypergraph is a coloring of the vertices such that no hyperedge is monochromatic. The strong/weak chromatic number of a hypergraph is the minimum number of colors in a strong/weak coloring of the hypergraph. Our question has been completely answered for the weak chromatic number, similarly to the graph case. We characterize the hypergraphs $F$ such that $F$-free hypergraphs have bounded strong chromatic number. The only remaining case is when $F$ is the 3-uniform expansion $S_k^+$ of a star with $k$ edges. Concerning the strong chromatic number of $S_k^+$-free hypergraphs, we give bounds that are asymptitically sharp as $k\rightarrow\infty$. We also consider the same problem when the Berge copies of a graph $F$ are forbidden. We characterize when the strong/weak chromatic numbers are bounded in this case, and obtain sharp results or bounds for specific trees. In particular, when $F$ is a path, we give a tight bound when $r=3$ and an asymptotically sharp bound when $r=4$.

The spin angular momentum (SAM) of light has become a cornerstone of numerous photonic applications, including optical communication and chiral photonics. Because SAM is inherently associated with circularly polarized light (CPL), the ability to modulate CPL in a controlled and efficient manner is essential not only for advancing fundamental studies of light-matter interactions but also for enabling next-generation photonic technologies. However, such modulation is commonly realized by structurally chiral systems, which inherently limits the feasibility of dynamic tuning. Here, we demonstrate that one-dimensional plasmonic crystals (1D PlCs), despite their structural symmetry, can serve as a platform for controllable CPL generation. By employing an electron beam in scanning transmission electron microscopy (STEM), we coherently excite transition radiation and emission from 1D PlC modes. Their interference produces energy- and momentum- (emission angle-) resolved CPL, which clearly reveals its dispersion and spatial dependence at the nanoscale, providing direct guidance for its manipulation and offering insights into the design of plasmonic devices including the phase information. Furthermore, interference with surface plasmon polariton scattering at the structural boundary enables the efficiency modulation of CPL generation via the excitation position along the terrace.

Treatment effect distributions are not identified without restrictions on the joint distribution of potential outcomes. Existing approaches either impose rank preservation -- a strong assumption -- or derive partial identification bounds that are often wide. We show that a single scalar parameter, rank stickiness, suffices for nonparametric point identification while permitting rank violations. The identified joint distribution -- the coupling that maximizes average rank correlation subject to a relative entropy constraint, which we call the Bregman-Sinkhorn copula -- is uniquely determined by the marginals and rank stickiness. Its conditional distribution is an exponential tilt of the marginal with a Bregman divergence as the exponent, yielding closed-form conditional moments and rank violation probabilities; the copula nests the comonotonic and Gaussian copulas as special cases. The empirical Bregman-Sinkhorn copula converges at the parametric $\sqrt{n}$-rate with a Gaussian process limit, despite the infinite-dimensional parameter space. We apply the framework to estimate the full treatment effect distribution, derive a variance estimator for the average treatment effect tighter than the Fréchet--Hoeffding and Neyman bounds, and extend to observational studies under unconfoundedness.

Clustering multivariate binary data is of interest in many scientific fields, including ecology, biomedicine, and social policy. Beyond heuristic clustering algorithms, such data can be modelled using multivariate Bernoulli mixture models. Many Bayesian implementations of these models involve a trade-off between computational efficiency and full posterior inference. We propose instead a Bayesian approach able to provide both aspects. The method fixes the total number of components to a large value and employs an asymmetric Dirichlet prior on the mixture weights. The asymmetric Dirichlet hyperparameters are elicited using the popular Penalized Complexity prior framework, which provides an intuitive way for users to inform the induced distribution of the number of clusters. An efficient MCMC algorithm is then developed to fit the model. Simulations and real-world applications demonstrate that the method is competitive with existing alternatives and can outperform them in certain settings. The proposal is illustrated using an ecological dataset about presence-absence of species across multiple sites, where cluster-specific parameters are modelled on the basis of environmental conditions. Overall, the proposed method provides a computationally efficient, fully Bayesian, and interpretable framework for clustering multivariate binary data, with potential applications across diverse scientific domains.

The matrix completion problem provides a unifying lens through which many fundamental problems in coding theory can be viewed. In this paper, we investigate Locally Recoverable Codes (LRCs) with Maximal Recoverability (MR) and Maximum Distance Profile (MDP) convolutional codes in the framework of matrix completion. In particular, we present techniques that are general enough to provide constructions for both types of codes. A common feature of our code constructions is the sparsity of their generator matrices and the property that a large number of the entries of the generator matrices are elements of a small subfield of a larger extension field.

We show that surface waves in a draining-bathtub vortex provide a hydrodynamic realization of both Aharonov-Bohm phase shifts and Lense-Thirring frame dragging within a single system. A static time transformation maps the flat (2+1)-dimensional wave equation onto the convected shallow-water equation, yielding an effective vector potential set by the background flow. In this geometry, the circulation defines a global phase holonomy that controls wave structure. Traveling waves exhibit wavefront dislocations characteristic of Aharonov-Bohm scattering, while standing-wave superpositions produce nodal patterns that rotate at an angular velocity fixed by the circulation, providing a direct analogue of frame dragging. For noninteger circulation, the problem is naturally defined on the universal cover, ensuring single-valued partial-wave solutions. Experiments on a controlled vortex confirm these predictions and establish a laboratory platform in which topological phase and inertial effects, central to gauge and gravitational physics, emerge from a measurable velocity field.

This paper addresses characterizations of Integral Input-to-State Stability (iISS) for hybrid systems with memory. Based on the Krasovskii approach, a novel Lyapunov characterization of iISS is established to extend the hybrid system theory to the time-delay case. In particular, we introduce the notions of dissipativity, detectability and storage functional to describe the iISS property from different perspectives. Under mild regularity and convexity assumptions, the equivalence relations among diverse stability descriptions are established, which lays a solid foundation for the control design. Finally, a numerical example is presented to illustrate the derived results.

Chiral spin textures such as skyrmions have attracted considerable attention due to their nontrivial topology, chirality, stability at the nanoscale, and potential for low-power spintronic devices. The recent discovery of intrinsic magnetism in van der Waals (vdW) materials and the ability to engineer their heterostructures has opened a new platform to study and manipulate such textures. In these layered systems, atomically sharp interfaces, strong spin-orbit coupling, and tunable symmetry breaking provide unique opportunities to stabilize and control chiral magnetic states. This review summarizes the fundamental mechanisms underlying the formation of chiral spin textures in vdW heterostructures, including the roles of exchange interactions, magnetic anisotropy, Dzyaloshinskii-Moriya interaction, and dipolar effects. We highlight key experimental advances in the observation and manipulation of chiral textures, discuss their dynamical properties and transport signatures, while overviewing selected theoretical investigations. Finally, we outline current challenges and future directions toward realizing robust, room-temperature chiral spin textures for practical spintronic technologies.

Particle filters (PFs) are recursive Monte Carlo algorithms for Bayesian tracking and prediction in state space models. This paper addresses continuous-discrete filtering problems, where the hidden state evolves as an Itô stochastic differential equation (SDE) and observations arrive at discrete times. We propose a novel class of constrained PFs that enforce compact support on the state at each observation instant, thereby limiting exploration to plausible regions of the state space. Unlike earlier approaches that truncate the likelihood, the proposed method constrains the dynamics directly, yielding improved numerical stability. Under standard regularity assumptions, we prove convergence of the constrained filter, derive uniform-in-time error estimates, and extend the analysis to account for discretisation errors arising from numerical SDE solvers. A numerical study on a stochastic Lorenz-96 system demonstrates the practical application of the methodology when the constraint is implemented via barrier functions.